Immune decomposition and decomposability analysis of complex design problems with a graph theoretic complexity measure

Large scale problems need to be decomposed for tractability purposes. The decomposition process needs to be carefully managed to minimize the interdependencies between sub-problems. A measure of partitioning quality is introduced and its application in problem classification is highlighted. The measure is complexity based (real complexity) and can be employed for both disjoint and overlap decompositions. The measure shows that decomposition increases the overall complexity of the problem, which can be taken as the measure’s viability indicator. The real complexity can also indicate the decomposability of the design problem, when the complexity of the whole after decomposition is less than the complexity sum of sub-problems. As such, real complexity can specify the necessary paradigm shift from decomposition based problem solving to evolutionary and holistic problem solving